A five-time Oscar nominee, he was known for playing many different characters, with his list of films including Erin Brockovich, Big Fish, Scrooge, Annie and Murder On The Orient Express.
He most recently starred in the James Bond film Skyfall and the Bourne films in a career spanning almost 60 years.
In a statement, his family said: “Albert Finney, aged 82, passed away peacefully after a short illness with those closest to him by his side. The family request privacy at this sad time.”
Born in Salford in 1936, Finney took to the stage at an early age and, despite his “humble origins”, went on to earn a place at the Royal Academy of Dramatic Arts in London.
He made his film debut with a small part in The Entertainer in 1960.
Director Tony Richardson then cast him in the lead roles in kitchen-sink drama Saturday Night and Sunday Morning, and Tom Jones – for which he earned his first Oscar nomination, for best actor.
He went on to play the title role in Scrooge and Hercule Poirot in Murder On The Orient Express, which garnered his second nomination, as well as Daddy Warbucks in Annie.
Known for his versatility, he played a huge range of characters during his years on screen, from Winston Churchill to Pope John Paul II.
Further Oscar nods came for The Dresser and Under The Volcano in 1984 and 1985, and then again for best supporting actor for playing lawyer Ed Masry in Erin Brockovich, starring opposite Julia Roberts.
As the gruff Scotsman Kincade in Skyfall, he starred alongside Daniel Craig as James Bond and Judi Dench as M.
Actor David Morrissey is among those paying tribute on social media, writing: “One of the true great. Both on stage and screen. A powerhouse of an actor. A real hero of mine. RIP Albert Finney”.
BAFTA has also remembered the star, who was honoured with a BAFTA fellowship in 2001.
“We are deeply saddened to hear of the passing of Albert Finney,” a statement said. “The recipient of the BAFTA Fellowship in 2001, Finney will be warmly remembered for his powerful performances in Saturday Night And Sunday Morning, Tom Jones, Big Fish and many more.”
The British Film Institute said it was “saddened” to learn of Finney’s death.
Finney is survived by his third wife, Pene, son Simon and two grandchildren.